Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×C127⋊C32 |
| unambiguous semidirect product | (C2×C127)⋊C32 |
| derived, Sylow | C127 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D127 |
| commutator, hypocenter | C127 | C2×C32 |
| Frattini | C16 | C2×D127 |
| Fitting | C2×C16×C127 | C2 |
| socle | C22×C127 | C16 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2×C16 | |
34 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic127, C4×C127⋊C32, #30636863, … |
| maximal normal subgroup of | C32×Dic127, C4×C127⋊C32, #30636863, … |
| maximal quotient of | C4×C127⋊C32, C22⋊(C127⋊C32), C4⋊(C127⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 381);